Question

A cylindrical vessel contains $49.896$ litres of liquid, cost of painting its CSA at $2$ paise/sq.cm is Rs $95.04$. Then its total surface area is ........

• A. $5724$ ${cm}^2$
• B. $7524$ ${cm}^2$
• C. $5742$ ${cm}^2$
• D. none of the above

Answer 1

Answer: (B)

$7524$ ${cm}^2$

Given, volume of cylindrical vessel $=49.896$ litres $=49896$ $c{m}^3$ ..... [As 1 litre = 1000 $c{m}^3$] and

cost of painting its CSA at $2$ paise/square cm $=$ Rs $95.04$

$\Rightarrow CSA=\frac{95.04}{0.02}=4752{cm}^2$

Now, let $r$ and $h$ be the radius and height of the cylindrical vessel respectively.

According to the given condition,

$\Rightarrow 2\pi rh=4752$ .... (1)

and $\pi r^{2}h=49896\Rightarrow \frac{2\pi rh}{\pi r^{2}h}=\frac{4752}{49896}\Rightarrow \frac{2}{r}=\frac{594}{6237}\Rightarrow r=21$ cm

Putting the value of $r$ in (1), we get

$2\times \frac{22}{7}\times 21\times h=4752\Rightarrow h=36$ cm

So, total surface area of the cylindrical vessel $=2\pi rh+2\pi r^2$

$=2\pi r(h+r)$

$=2\times \frac{22}{7}\times 21(21+36)$

$=7524{cm}^2$